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The rational homotopy of Thom spaces and the smoothing of isolated singularities. (English) Zbl 0563.57010
Rational homotopy methods are used for studying the problem of the topological smoothing of complex algebraic isolated singularities. It is shown that one may always find a suitable covering which is smoothable. The problem of the topological smoothing (including the complex normal structure) for conical singularities is considered in the sequel. A connection is established between the existence of certain relations between the normal Chern degrees of a smooth projective variety and the question of its realization as a linear section (not necessarily hyperplane).
57R10 Smoothing in differential topology
32Sxx Complex singularities
55P62 Rational homotopy theory
32S05 Local complex singularities
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